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yawa3891 [41]
3 years ago
11

Find the inverse of the radical function

t[3]{x-2}" alt="\sqrt[3]{x-2}" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
kolezko [41]3 years ago
4 0

Answer: y=x³+2 or f⁻¹(x)=x³+2

Step-by-step explanation:

To find the inverse of the radical function, we replace y with x and x with y. Then, you solve for y.

y=\sqrt[3]{x-2}                        [replace y with x and x with y]

x=\sqrt[3]{y-2}                        [cube both sides to cancel out the cubed root]

x^3=y-2                          [add both sides by 2]              

x^3+2=y

Now that we have switched the variables and solved for y, we know that the inverse function is y=x³+2 or f⁻¹(x)=x³+2.

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Use the quadratic formula to solve the equation
azamat

Answer:

=3

=2

Step-by-step explanation:

12−5+6=0

using the Quadratic Formula where

a = 1, b = -5, and c = 6

=−±2−4‾‾‾‾‾‾‾‾√2

=−(−5)±(−5)2−4(1)(6)‾‾‾‾‾‾‾‾‾‾‾‾‾‾√2(1)

=5±25−24‾‾‾‾‾‾‾√2

=5±1‾√2

The discriminant 2−4>0

so, there are two real roots.

Simplify the Radical:

=5±12

=62=42

which becomes

=3

=2

hope this helps :)

7 0
3 years ago
Ayden had a goal of finishing painting at least 80%, percent of the 500square meters of a house's walls by today. He actually fi
choli [55]

Answer:

yes Ayden Painted 415 square meters more than his goal

7 0
3 years ago
Factor using the distributive property using the GCF <br> 10x-35
wlad13 [49]

Answer:

5(2x-7)

Step-by-step explanation:

7 0
2 years ago
The parking lot for a hotel should have 114 parking spaces. If ech row can have 13 parking spaces, then the minimum nukber of ro
MArishka [77]

So @mathmate deleted my comment because "I wasn't explaining my answer" well I did

I clearly stated that you have to make educated guess and I showed how I GOT my answer

so i guess here is my "proper" answer

There is no specific formula for this, so you can make an educated guess

for example:

13*5 = 65 (this isn't right because we need a minimum of 114)

so we continue the guessing

I then next tried

13*9

I got 117,

117 is more than 113

making 9 the minimum amount of rows for the hotel parking lot


there ya go @mathmate is that clear enough?

4 0
2 years ago
Radioactive Waste The rate at which radioactive waste is entering the atmosphere at time t is decreasing and is given by Pe^-kt,
Dmitry_Shevchenko [17]

Answer:

\displaystyle{\int^{\infty}_0 {50e^{-0.04t}}\, dt}=1250

Step-by-step explanation:

Given:

T =\displaystyle{\int^{\infty}_0 {Pe^{-kt}} \, dt}

where,

T = total amount of waste

P = 50, the initial rate

k = 0.04

t = time

T =\displaystyle{\int^{\infty}_0 {50e^{-0.04t}} \, dt}

now we need to solve this integral!

T =\displaystyle{50\int^{\infty}_0 {e^{-0.04t}} \, dt}

T = \left|50\left(\dfrac{e^{-0.04t}}{-0.04}\right)\right|^{\infty}_0

T = \left|-1250e^{-0.04t}\right|^{\infty}_0

T = (-1250e^{-0.04(\infty)})-(-1250e^{-0.04(0)})

when any number has a power of negative infinity it is 0. because: a^-{\infty} = \dfrac{1}{a^{\infty}} = \dfrac{1}{\infty} = 0, like something being divided by a very large number!

T = (-1250(0))-(-1250e^0)

T = 1250

this is the total amount of waste

6 0
2 years ago
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